vrieskortewegequation方程osnabrucksolitary TheKorteweg-deVriesEquation:History,exactSolutions,andgraphicalRepresentationbyKlausBrauer,UniversityofOsnabrück/Germany1LastRevisionofthispaper:February2014TravellingwavesassolutionstotheKorteweg-deVriesequation(KdV)whichisanon-linearPartialDifferentialEquation(PDE)ofthirdorderhav...
Here the basic paradigm is the well-known Korteweg-de Vries equation and its solitary wave solution. We present a brief historical discussion, followed by a typical derivation in the context of internal and surface water waves. Then we describe two extensions, the first to the variable-...
Derivation of Korteweg-de Vries flow equations from third order nonlinear Schröodinger equation.HamiltonianfunctionKdVequationMultipleScaleAnalysisNLSequationThe nonlinear Shrödinger equation with a third-order dispersive terms is considered. We perform a multiple scales analysis on the third order ...
KORTEWEG-de Vries equationThis paper investigates two different novel approaches to degenerate from normally interacting lump chains to anomalously interacting lumps for the generalized Korteweg鈥揹e Vries equation. The first direct degeneracy method is to derive the anomalously int...
Sequel to this, the subalgebras and combination of the achieved symmetries are invoked in the reduction process which enables the derivation of nonlinear ordinary differential equations associated with the generalized geophysical Korteweg-de Vries equation under study. Most of the achieved n...
Korteweg-de Vries equationWhitham modulation theoryPerturbation theoryOriginal Whitham's method of derivation of modulation equations is applied tosystems whose dynamics is described by a perturbed Korteweg-de Vries equation.Two situations are distinguished: (i) the perturbation leads to appearance ofright...
CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of the Burgers and Korteweg–de Vries–Burgers EquationsComputer algebra systemKorteweg–de Vries–Burgers equationderivation of the formulas of the analytic-numerical algorithm...
Derivation of Korteweg-de Vries flow equations from derivative nonlinear Schrodinger equation.We derive, as amplitude equations, Korteweg-de Vries (KdV) flow equations in the bi-Hamiltonian form by performing a multiple scales analysis on the derivative nonlinear Schrdinger (DNLS) equation in the ...
The method of multiple scales or multitiming technique is used to derive the variable coefficient Korteweg de Vries (KdV) equation. Three small and independent parameters are introduced, epsilon which gives a measure of the amplitude of the wave, micrometers which gives a measure of the ...
We derive Korteweg–de Vries (KdV) flow equation in the bi-Hamiltonian form as an amplitude equation.doi:10.1016/j.amc.2011.07.045Mehmet Naci ?zerMurat KoparanElsevier Inc.Applied Mathematics and ComputationN.O. Mehmet, K. Murat, Derivation of Korteweg-de Vries flow equations from the ...